Simone, if that other line runs separately to the exchange, it's a good idea. If it's on the same copper pair, forget it, you'll just tax the copper even more so you'll get two half-arsed connections. You can ask telstra for another copper pair, but they'll ask for your farm and the lives of your children in exchange I reckon.
If you have telstra 3G/4g reception, a good alternative maybe to get one of those telstra wireless modem / wifi hotspot devices, buy some pre-paid data and either put the family on it during race hours, or use it yourself.
The big catch:
pings are usually crap on these devices, and data is expensive. So you won't be too happy if you use it, and they'll chew through a lot of money watching videos on it. Sadly.